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Journal of Theoretical Probability

, Volume 22, Issue 1, pp 203–219 | Cite as

Stochastic Integration Based on Simple, Symmetric Random Walks

  • Tamás Szabados
  • Balázs Székely
Article

Abstract

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, the method gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not càdlàg in general.

Keywords

Stochastic integration Strong approximation Random walk Itô formula 

Mathematics Subject Classification (2000)

60H05 60F15 60G50 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsBudapest University of Technology and EconomicsBudapestHungary

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